Generalized joint model for robot manipulator kinematic calibration and compensation

A generalized model that goes beyond the usual assumption of “ideal” joint behavior is proposed. The “real” joint has five ancillary degrees of freedom besides the dominant motion. The resulting manipulator transformation with its greater degree of sophistication is expected to help in calibration and compensation of the various kinematic contributions to robot inaccuracy. The procedure to compute this generalized manipulator transformation is presented. The generalized model also results in manipulator differential relationships and these are discussed.     

Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific task requirements. However, the machining tolerance and assembly errors at the module interconnections affect the positioning accuracy of the end-effector. This article describes a novel kinematic calibration algorithm for modular robots based on recursive forward dyad kinematics. The forward kinematic model derived from the Product-of-Exponentials formula is configuration independent. The error correction parameters are assumed to be in the relative initial positions of the dyads. Two calibration models, namely the six- and seven-parameter methods, are derived on the grounds of the linear superposition principle and differential transformation. An iterative least square algorithm is employed for the calibration solution. Two simulation examples of calibrating a three-module manipulator and a 4-DOF SCARA type manipulator are demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitude after the calibration. © 1997 John Wiley & Sons, Inc.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

一种工业机器手的自适应阻抗控制方法

提出一种基于任务空间的直接自适应阻抗方法，它不要求辨识机器手动态模型结构和参数，不需要计算机器手的运动学逆变换，因此，避免了基于机器手模型线性参数辨识的控制方法的缺点。     

排爆机器人机械臂定位精度误差自动补偿方法研究

针对于排爆机器人在进行排除爆破物质时,机械臂不能满足绝对准确的定位要求,位置检测精度与实际距离之间存在一定的误差。为了解决这一问题,提出排爆机器人机械臂定位精度误差自动补偿方法。基于D-H运动模型和微分变换法创建排爆机器人机械臂位姿误差模型,对误差模型进行重复参数分析,去除重复参数获得可辨识的线性方程;在可辨识的运动学参数误差模型线性方程中加入一个增量进行误差补偿。最后通过仿真实验结果表明,所提方法通过对机械臂位姿误差模型进行有效补偿,使排爆机器人机械臂绝对定位精度均值提升1.3mm。     

Singularity-robust decoupled control of dual-elbow manipulators

The ability of a robot manipulator to move inside its workspace is inhibited by the presence of joint limits and obstacles and by the existence of singular positions in the configuration space of the manipulator. Several kinematic control strategies have been proposed to ameliorate these problems and to control the motion of the manipulator inside its workspace. The common base of these strategies is the manipulability measure which has been used to: (i) avoid singularities at the task-planning level; and (ii) to develop a singularity-robust inverse Jacobian matrix for continuous kinematic control. In this paper, a singularity-robust resolved-rate control strategy is presented for decoupled robot geometries and implemented for the dual-elbow manipulator. The proposed approach exploits the decoupled geometry of the dual-elbow manipulator to control independently the shoulder and the arm subsystems, for any desired end-effector motion, thus incurring a significantly lower computational cost compared to existing schemes.     

Simultaneous kinematic calibration,localization, and mapping (SKCLAM) for industrial robot manipulators†

Recently, the demand for more accurate, productive, and economical robot manipulators is increasing in the robotics industry. However, a manipulator will produce kinematic errors during production. Thus low-cost kinematic calibration is demanded. Moreover, environmental mapping is also demanded to plan the motions of the manipulator. In this paper, we proposed a simultaneous kinematic calibration, localization, and mapping (SKCLAM) method, which can simultaneously calibrate the kinematic parameters of an industrial robot manipulator using a commercial RGB-D camera attached to its end effector to reconstruct its surroundings. In our method, the kinematic calibration is achieved with feature detection and epipolor geometry. Synthetic and real data experiments were conducted to verify the SKCLAM method. We succeeded in reducing the kinematic errors of the manipulator and reconstructing dense 3D maps of the workspace in the experiments.     

Adaptive unified motion control of mobile manipulators

This paper presents a unified motion controller for mobile manipulators which not only solves the problems of point stabilization and trajectory tracking but also the path following problem. The control problem is solved based on the kinematic model of the robot. Then, a dynamic compensation is considered based on a dynamic model with inputs being the reference velocities to the mobile platform and the manipulator joints. An adaptive controller for on-line updating the robot dynamics is also proposed. Stability and robustness of the complete control system are proved through the Lyapunov method. The performance of the proposed controller is shown through real experiments.     

Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates

A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc.     

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.     

Li-function activated ZNN with finite-time convergence applied to redundant-manipulator kinematic control via time-varying Jacobian matrix pseudoinversion

This paper presents and investigates the application of Zhang neural network (ZNN) activated by Li function to kinematic control of redundant robot manipulators via time-varying Jacobian matrix pseudoinversion. That is, by using Li activation function and by computing the time-varying pseudoinverse of the Jacobian matrix (of the robot manipulator), the resultant ZNN model is applied to redundant-manipulator kinematic control. Note that there are nine novelties and differences of ZNN from the conventional gradient neural network in the research methodology. More importantly, such a Li-function activated ZNN (LFAZNN) model has the property of finite-time convergence (showing its feasibility to redundant-manipulator kinematic control). Simulation results based on a four-link planar robot manipulator and a PA10 robot manipulator further demonstrate the effectiveness of the presented LFAZNN model, as well as show the LFAZNN application prospect.     

A comparison between the Denavit–Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators

This paper aims to integrate didactically some engineering concepts to understand and teach the screw-based methods applied to the kinematic modeling of robot manipulators, including a comparative analysis between these and the Denavit–Hartenberg-based methods. In robot analysis, kinematics is a fundamental concept to understand, since most robotic mechanisms are essentially designed for motion. The kinematic modeling of a robot manipulator describes the relationship between the links and joints that compose its kinematic chain. To do so, the most popular methods use the Denavit–Hartenberg convention or its variations, presented by several author and robot publications. This uses a minimal parameter representation of the kinematic chain, but has some limitations. The successive screw displacements method is an alternative representation to this classic approach. Although it uses a non-minimal parameter representation, this screw-based method has some advantages over Denavit–Hartenberg. Both methods are here presented and compared, concerning direct/inverse kinematics of manipulators. The differential kinematics is also discussed. Examples of kinematic modeling using both methods are presented in order to ease their comparison.     

Perfomance-based adaptive tracking control of robot manipulators

This article presents two new adaptive schemes for the motion control of robot manipulators. The proposed controllers are very general and computationally efficient because they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that in the absence of disturbances the ultimate bound on the size of the tracking errors can be made arbitrarily small. Computer simulation results are given for a PUMA 560 manipulator, and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers. Experimental results are presented for an IMI Zebra Zero manipulator and confirm that the control schemes provide a simple and effective means of obtaining high-performance trajectory tracking. © 1995 John Wiley & Sons, Inc.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.     

Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

Gravity compensation of spatial two‐DOF serial manipulators

This article presents the analysis of gravity compensation of a two‐DOF serial manipulator operating in three‐dimensional space by means of linear spring suspension. The physical configuration of the serial manipulator is assumed general. The analysis begins with gravity compensation of a one‐DOF manipulator in order to form the basis which is then extended to a two‐DOF manipulator. The approach taken in the analysis is that of conservation of potential energy. The goal is to seek the location and the stiffness of springs that provide complete compensation of gravity in the manipulator system. It has been found that complete compensation of gravity in a two‐DOF serial manipulator system is possible. Unlike many previous works on spring suspension of a rigid body, which assume that one end of the suspending spring is attached to ground, it is proven in this study that, for complete compensation in a two‐DOF manipulator, the spring that suspends the distal link cannot be connected to ground. Instead, it must be in certain motion relative to the proximal link. The discussion on how to provide such a motion for the spring is given. It is also explained how the problem of gravity compensation of a robot manipulator can be shifted to that of changing gravity environment within a manipulator system. The concept can be applied to simulation and testing of robot manipulators that will be sent to operate in a different gravity environment, such as space. © 2002 Wiley Periodicals, Inc.     

Error-model-based robot calibration using a modified CPC model

Selection of a proper robot kinematic model is a critical step in error-model-based robot calibration. The Denavit-Hartenberg (DH) model exhibits singularities in calibration of robots having consecutive parallel joint axes. The complete and parametrically continuous (CPC) modeling technique is one of the more versatile alternative modeling conventions designated to fit the needs of manipulator calibration. No modeling convention is, however, perfect. One “user-unfriendly” aspect of the CPC model is a condition handling technique needed, when constructing the error model, to avoid model singularities due to the adoption of the direction vectors of the joint axes as link parameters.This paper presents a modification to the CPC model which brings the model closer to the DH model. Rather than using the direction vectors of joint axes, the modified CPC (MCPC) model employs angular parameters to acommodate the required rotations for each link transformation. This modification results in a much simplified error model. The model, like the CPC model, is capable of completely describing the geometry and motion of the manipulator in a reference coordinate frame. Its error model possesses a minimum number of parameters to span the entire geometric error space and it can be made singularity-free by proper selection of the tool axis. This paper presents a calibration study of the PUMA robot using the MCPC model. A moving stereo camera system was employed for end-effector pose measurements. The MCPC error model was then used for kinematic identification. Results on the PUMA arm show that the MCPC performs well for robot calibration. The well-defined structure and user friendliness of the MCPC model may facilitate the implementation of robot calibration techniques on the factory floor.     

Kinematic aspects of a robot-positioner system in an arc welding application

This paper focuses on the kinematic control of a redundant robotic system taking into account particularities of the arc welding technology. The considered system consists of a 6-axis industrial robot (welding tool manipulator) and a 2-axis welding positioner (workpiece manipulator) that is intended to optimise a weld joint orientation during the technological process. The particular contribution of the paper lies in the area of the positioner inverse kinematics, which is a key issue of such system off-line programming and control. It has been proposed a novel formulation and a closed-form solution of the inverse kinematic problem that deals with the explicit definition of the weld joint orientation relative to the gravity. Similar results have also been obtained for the known problem statement that is based on a unit vector transformation. For both the cases, a detailed investigation of the singularities and uniqueness-existence topics have been carried out. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.     

“妙手”系统机械结构设计与优化

为了辅助医生更好地完成显微外科手术,开发了一种主从异构的显微外科手术机器人系统——“妙手”系统．“妙手”系统的主手为商业化的Phantom Desktop主手,从手为针对显微外科血管缝合而设计的“妙手”从手．从手包括位置机构和姿态机构．位置机构通过丝传动实现双四连杆机构的运动特性;姿态机构采用三轴交汇于一点的设计思想．通过分析双四连杆机构的运动特性,根据Angeles运动灵活度指标对双四连杆机构进行了优化．结果表明：当双四连杆机构前三级杆等长且I级杆与III级杆垂直时,机构运动灵活度取最大值．     

Parallel and distributed trajectory generation of redundantmanipulators through cooperation and competition among subsystems

Autonomous distributed control (ADC) is one of the most attractive approaches for more versatile and autonomous robot systems. The paper proposes a parallel and distributed trajectory generation method for redundant manipulators through cooperative and competitive interactions among subsystems composing the ADC that is based on a concept of virtual arms. The virtual arm has the same kinematic structure as the manipulator except that its end point is located on a joint or link of the manipulator. Then the redundant manipulator can be represented by a set of the virtual arms. Trajectory generation and point to point control of the redundant manipulator are discussed, and it is shown that the kinematic redundancy of the manipulator can be utilized positively in the generated trajectories by using the virtual arms.